5.3.3. Verification of Graphic Sequence

Try these first

1. 1.

   Define degree sequence.

   Hint

   Think about what degree refers to in graphs.

2. 2.

   What must be true about the degrees in a graphic sequence?

   Hint

   Consider if negative degrees make sense in graph theory.

3. 3.

   What defines a graphic sequence?

   • A sequence where all degrees are even.
   • A sequence that can form a simple graph.
   • A sequence listed in random order.

   Hint

   Think about the properties of graph representation.

4. 4.

   True or False: The sum of the degrees in a graphic sequence can be odd.

   • True
   • False

   Hint

   Reflect on how edges are connected to vertices.

5. 5.

   Prove that the sequence (3, 3, 3, 1) is graphic, using systematic reduction.

   Hint

   Take steps to verify each reduction.

6. 6.

   Design a sequence of your own that is non-graphic and explain why it fails the graphic tests.

   Hint

   Check the sum of your proposed sequence.